The last interesting problem where Darboux–Halphen system appears is in the context of a 3-dimensional Frobenius manifold with a certain potential function \(F(t)\) . Frobenius manifold arose as a geometrization of Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations [1]}, [2]}, an overdetermined system of differential equations that appear in the physics of topological field theories in 2 dimensions. In this particular case of dimension 3, the WDVV equation is known as Chazy equation, which has a close tie with the solutions of Darboux system. We present it in Section , where we follow Dubrovin's notes [3]}, [4]}.
